Sen. Mike Lee, R-Utah, said he would vote in favor of the GOP's healthcare bill if a proposal he introduced would be added to the legislation.

Lee and Sen. Ted Cruz, R-Texas, recently introduced the Consumer Freedom Amendment, which they said would give Americans more choices while shopping for healthcare plans.

Lee spoke with Fox News Thursday morning and said if that option is included in the Senate GOP's healthcare bill, he would be a yes vote.

"It's time to offer the American people the chance to connect with willing insurers to buy the policy that's right for them. This amendment would leave other protections in place for those who need them, but it would also create other options for those who want them," Lee said.

"All things being equal, if they could get that, I could get to yes. Now I speak only for myself. I control only my vote. But what I'm saying is all things being equal, if they added that with those protections, the protections of the dual pool, the fully loaded Consumer Freedom Amendment, I could get to yes."

Republicans' efforts to repeal and replace Obamacare have stalled in recent days, with multiple lawmakers in the party saying they would not vote for the Better Care Reconciliation Act. If Senate leaders are able to cobble together a version of the bill that is more appealing to members, it's unclear when a floor vote could occur because of the absence of Sen. John McCain, R-Ariz., who was diagnosed with brain cancer this week.